Drinking containers which hold consumable liquids are well known in the art. Such containers include full open mouthed containers such as glasses and cups, as well as partially open mouthed containers such as cans and bottles. The drinking containers can be of various shapes such as cylindrical, square, hexagonal, octagonal, frustoconical (tapered) or other shapes. It is also know to place a close-fitting sleeve around the drinking container. The sleeve serves as an insulator to both maintain the temperature of the beverage within the container, and in the case of hot beverages, to protect the hand of a user from possible burns. The sleeves are typically made from foam, neoprene, polyester, vinyl or the like and are somewhat elastic so that they grip the drinking container. Other sleeve materials can include paper or fabric. The outside surface of the sleeves can contain advertising or other indicia.